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Question

The mean weight of $$9$$ items is $$15$$. If one more item is added to the series the mean becomes $$16$$. The value of the $$10^{th}$$ item is


A
35
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B
30
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C
25
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D
20
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Solution

The correct option is C $$25$$
Assuming original nine elements are $$x_1, x_2, x_3, .........x_9$$ and new element is $$x$$
Sum of original nine elements is $$\displaystyle\sum_{i=1}^9x_i =9\times 15=135$$
Given new mean after addition of $$x$$ is 16. $$\Rightarrow \cfrac{\displaystyle \sum_{i=1}^9x_i + x}{10} = 16$$
$$\Rightarrow \cfrac{135+x}{10}=16 \Rightarrow  x= 160-135 = 25$$

Mathematics

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